Principles of Thermodynamics and Statistical Mechanics

D. F. Lawden

• Publisher: Dover Publications
• Year: 2013
• Print ISBN:
  9780486446479
• eBook ISBN:
  9780486152240
• Topic: Physical Sciences
• Subtopic: Physics
• Index: Physics

A thorough exploration of the universal principles of thermodynamics and statistical mechanics, this volume explains the applications of these essential rules to a multitude of situations arising in physics and engineering. It develops their use in a variety of circumstances—including those involving gases, crystals, and magnets—in order to illustrate general methods of analysis and to provide readers with all the necessary background to continue in greater depth with specific topics.
Author D. F. Lawden has considerable experience in teaching this subject to university students of varied abilities and backgrounds. Well acquainted with which concepts and arguments sometimes prove problematic, he presents the potentially difficult sections with particular care. Students can supplement their understanding by working through the numerous exercises which appear throughout the text. Mathematical physicists will find this volume of particular value, as will engineers requiring a basic but comprehensive introduction to the principles of thermodynamics and statistical mechanics.

CHAPTER 1

Classical thermodynamics

1.1 Thermodynamics and statistical mechanics

Thermodynamics is the branch of physics which studies the manner in which the properties of substances are dependent upon their temperatures. The classical theory was developed during the nineteenth century and succeeded in identifying the quantities needed to describe the thermodynamic state of a body (e.g. temperature, pressure, entropy, etc.) and in predicting the manner in which these will vary when substances in different states interact by mixing or by being placed in thermal contact with one another. Coefficients (e.g. specific heat) were defined whose values determined the thermal properties of a substance, but it was necessary to determine these values empirically—the theory provided no means by which they could be deduced from other physical properties of the substance, such as its crystalline structure. In particular, the theory took no account of the molecular constitution of substances and the mechanical or electromagnetic properties of the particles from which they are composed. The possibility that the thermodynamic behaviour of matter might be explained as a consequence of the mechanical behaviour of its constituent molecules, was first successfully exploited by Clerk Maxwell (1831–79) and later formed the basis for a new theory called statistical mechanics, which was created by Ludwig Boltzmann (1844–1906). Thus the principles of classical thermodynamics have been shown to be derivable from the more fundamental principles of mechanics and electromagnetism. Nevertheless, the derived principles remain of prime importance for physics and it is still sensible to study them in isolation, before exhibiting them as elements of a more comprehensive, and thus necessarily more complex, theory. By this means, they will be brought to the centre of the reader’s attention and the mathematical relationships connecting them will be emphasized.

In this and the following chapter, the elements of the classical theory will accordingly be constructed upon a foundation of experimental facts relating to the macroscopic properties of materials alone and no reference will be made to microscopic properties associated with their molecular structures. In subsequent chapters, we will demonstrate how these principles arise from a consideration of the mechanical behaviour of atoms and molecules and how the thermal characteristics of a substance can be predicted from a knowledge of its microscopic structure.

1.2 Thermodynamical equilibrium

The theory we are about to develop applies to the widest possible variety of physical systems; these may be homogeneous or heterogeneous and include solids, liquids and gases (and even radiation) which are mixed together or separated from one another in containers. However, it will almost always be assumed that the system under study has arrived at a state of equilibrium, in the sense that the macroscopic properties of its constituents are not observed to change as further time elapses. The properties here referred to are those such as density, pressure, temperature, magnetization, etc. which can be measured by instruments which do not probe the microscopic structure of the system. It is now well understood that this thermodynamical equilibrium, as it is termed, is superficial and is compatible with a rapid variation in the state of the system at the microscopic level of its constituent molecules. Thus if a system comprising a colloidal suspension of solid particles in a liquid is allowed to reach thermodynamic equilibrium in a vessel kept at a uniform temperature, a microscopic examination of the particles reveals that they are propelled into random motions by the bombardment they receive from surrounding liquid molecules (Brownian motion) and thus that the equilibrium at the macroscopic level is of a statistical nature and is not absolute. Such microscopic fluctuations are ignored by the classical theory, but can be treated by the more fundamental methods of statistical mechanics.

A system may approach equilibrium either by being placed in a container which shields it from all external influences (e.g. a Dewar’s flask), or by being permitted to interact with a steady environment through the walls of its container. In the former circumstances, the system is said to be isolated and the walls of the container to be adiabatic. In the latter case, the system is said to be in thermal contact with its surroundings and the walls to be diathermal. We shall often be supposing that the temperature of the system is known and this will imply that it has been placed in thermal contact wit...

Table of contents

• DOVER BOOKS ON PHYSICS
• Title Page
• Copyright Page
• Table of Contents
• Preface
• List of constants
• CHAPTER 1 - Classical thermodynamics
• CHAPTER 2 - Applications of classical theory
• CHAPTER 3 - Classical statistics. Maxwell’s distribution
• CHAPTER 4 - Method of mean values
• CHAPTER 5 - Quantum statistics
• CHAPTER 6 - Crystals and magnets
• CHAPTER 7 - Bose–Einstein and Fermi–Dirac statistics
• Appendices
• Bibliography
• Index